Matching Number and Induced Matching Number on a Graph

Tóm tắt báo cáo

Let G be a simple graph. A matching in G is a set of edges no two of which share an endpoint. An induced matching in G is a matching such that no two edges in the matching are joined by any third edge of the graph; that is, an induced matching is a matching which forms an induced subgraph. The largest cardinality of the (induced) matchings is called (induced) matching number.
This talk is aimed at surveying the important results of these numbers. We also gives the explicit formulas for the (induced) matching number of the corona graph G ◦ H, where H = {Hv : v ∈ V (G)} is a family of nonempty graphs indexed by the vertex set of a graph G. In addition, an issue pertaining to the graph G ◦ H, such as the Castelnuovo–Mumford regularity, will also be presented. These stem from a joint work with Pham My Hanh Pham and Tran Nam Trung.